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Red light keeps blinking not allowing you to press a button. Others report the same problem. Usually, the latent heat released in the deep convection warms up the entire tropospheric column with a maximum in the middle troposphere. The congestus clouds warm up the lower troposphere but cool down the upper troposphere. In contrast, the stratiform clouds warm up the upper troposphere and cool down the lower troposphere Mapes ; Khouider and Majda , ; Waite and Khouider We have assumed that for the 2-day waves, the stratiform and congestus heating are equal, and each one occupies one-third of the deep convective heating i.
The diabatic heating Q j can be represented by where H j is an arbitrary positive constant. This is based on a conception that has observational support for the 2-day waves Haertel and Kiladis ; Haertel et al. The negative heating is a simplification for dealing with the anomalous heating, and it represents a suppressed phase of 2-day waves similar to that shown in observations Haertel and Kiladis The standard nondimensional is close to 0.
Observations also show that the moisture perturbation has a comparable nondimensional magnitude with that of the temperature perturbation for the 2-day waves Takayabu et al. For example, the temperature and moisture perturbation amplitude is 0.
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The moisture anomalies are stronger than the temperature anomalies. For simplicity, we introduce a parameter a q to represent this nondimensional ratio, and represent. Substituting Eqs. From Eq. So the solution of 2-day waves can be obtained for the forcing 22 : where Eqs.
These solutions [Eqs. The pronounced backward tilt is well reproduced Fig. The upward motion is usually in phase with the positive heating source. In this solution, not only the structures but also the amplitudes are in accord with the observations Haertel and Kiladis For example, for the given heating amplitude of 6. Velocity vectors and contours of synoptic-scale a heating red and cooling blue , b temperature, and c moisture perturbations above the equator as functions of zonal and pressure coordinates for the eastward-tilted 2-day waves.
Contour interval is one-third of the perturbation amplitude. The contours and vectors are scaled to their respective maximum magnitudes: a 6.
From Eqs. Different from the solution derived under the geostrophic approximation, which has an off-equatorial maximum temperature perturbation Majda and Biello , the disturbances under the ageostrophic approximation here are all trapped near the equator Fig.
As such, our new solution for the 2-day waves may provide a strong EHT, which is not negligible compared with the momentum transfer. In the lower troposphere hPa , the temperature perturbations are nearly in phase with the zonal winds and lead the wave convergence Fig. The lower tropospheric disturbances Fig. Velocity vectors and contours of synoptic-scale positive red and negative blue temperature perturbations as functions of zonal and meridional coordinates at a and b hPa.
Contour intervals are as in Fig.
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The contours and vectors are scaled to their respective maximum magnitudes: a 0. Based on the solution [Eqs. Details of the derivation are reported in appendix B. The upscale eddy property transfer is drawn in Fig.
The eastward-tilted 2-day waves produce a lower tropospheric easterly and an upper tropospheric westerly EMT. Because the 2-day waves are trapped near the equator Fig. The EHT tends to cool down the middle troposphere. In Fig. Different from the negative EHT, the EQT is always positive in the middle troposphere, which means that the 2-day waves tend to moisten the middle troposphere on the planetary scale.
The contours are scaled to their respective maximum magnitudes: a 1. The first baroclinic mode can represent the deep convection of the moist Kelvin waves very well Wang , which provides an easy way to understand the interaction in the moist Kelvin waves.
To study this interaction, we try to establish a simple baroclinic SI model, where the eddy flux envelope of the 2-day waves can be easily represented by the large-scale motions. Details of derivation for Eqs. For the first baroclinic mode, the EMT produces lower tropospheric easterly and upper tropospheric westerly Fig. Meanwhile the EQT tends to moisten the middle troposphere Fig.
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As in Fig. Like the EMT that can provide an instability source for the MJO Wang and Liu , our results here show that the strong EHT of the 2-day waves may also provide an instability source or sink for the planetary-scale motions. There is an easy way to discuss the first baroclinic interaction between the moist Kelvin waves and the 2-day waves. For the moist Kelvin waves, we neglect the temporal variation of the moisture perturbation [i. The truncated first baroclinic SI model can be obtained by substituting Eqs. To build a real two-way SI model, we have to find the relationship between the eddy flux envelope and the large-scale motions.
When the moist Kelvin waves meet with the 2-day waves, observations show that the 2-day waves are more enhanced near the convective complex of the moist Kelvin waves Fig. The 2-day waves also show asymmetric phase relationship with the large-scale motions, and they are more active to the east of the moist Kelvin wave or the MJO that has a Kelvin wave component Fig.
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After the strong convection associated with the passing Kelvin waves, the 2-day waves begin to decay in the region where the stratiform clouds prevail. The enhanced activity of the 2-day waves tends to coincide with, or shift a little bit to the east of, the short Kelvin waves, which tends to occur to the east of the MJO that has a long Kelvin wave component Fig.pathwayviewer.com/map7.php
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This implies a dependence of phase lag on wavelength. Based on observation 1 that the 2-day waves are controlled by the large-scale convective complex, we assume that the eddy flux envelope is proportional to the large-scale diabatic heating or the large-scale vertical pressure velocity.
By this assumption the strength of the 2-day waves is proportional to. Furthermore, based on observation 2 that the 2-day waves are more enhanced to the east of the moist Kelvin waves or the MJO that has a Kelvin wave component, we assume that the eddy flux envelope of the 2-day waves leads in the direction of eastward propagation the convection center of the moist Kelvin wave by a phase.
It is necessary to determine these two SI coefficients to complete the SI model. The moisture Eq. After dividing the latter by the former we can obtain. The nondimensional mean vertical moisture gradient is taken as 0. Compared with the observations Lin and Johnson ; Yanai et al. Our results also show that the 2-day waves with magnitude of 6. Dividing Eq.
Substituting Eq. The moist Kelvin waves without interaction with the 2-day waves dashed lines in Figs. Such free moist Kelvin waves propagate eastward fast dashed line in Fig. The dashed lines represent the free moist Kelvin waves, and the starred lines represent the SI moist Kelvin waves only interacting with EMT. Nondimensional e -folding scales as a function of wavelength. The e -folding scales are scaled to the Rossby radius of deformation.
Here is determined by Eq. The EMT provides an instability source for the moist Kelvin waves, especially on the short scales starred line in Fig. This upscale transfer-induced instability mainly comes from the projection of lower tropospheric easterly EMT on the lower tropospheric easterly of the moist Kelvin waves. The easterly EMT enhances the in-phase easterly of the moist Kelvin waves, but damps the out-of-phase westerly of the moist Kelvin waves.
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The negative EHT cools down the middle troposphere so as to damp the moist Kelvin waves, and it even overwhelms the positive role of EMT. In this SI model, the 2-day waves transfer the boundary layer moisture into the middle troposphere and enhance the deep convection associated with the moist Kelvin waves through the upscale EQT. For the observational 2-day waves, a q is usually greater than 1 Takayabu et al. The unstable moist Kelvin waves suffer a short wave blow-up in the absence of the heating due to the planetary boundary layer—induced moisture convergence Wang The 2-day waves also affect the phase speed of the moist Kelvin waves Fig.
The cause is the advective effect of the lower tropospheric easterly EMT. Substituting the EMT Eq.